1. Field of Invention
The current invention relates generally to apparatus, systems and methods for analyzing a spectrum of signals. More particularly, the apparatus, systems and methods relate to using filters to analyze the spectrum of a signal. Specifically, the apparatus, systems and methods provide for a proportional bandwidth spectrum analysis in a synthetic instrument.
2. Description of Related Art
A Synthetic Instrument (SI) based spectrum analyzer is a filter bank with specified bandwidth and spacing between spectral centers designed to span a spectral interval of interest. In communication system applications, the filter width and the spacing between centers are fixed. This matches the structure of communication system channelized bandwidth frequency assignments. This relationship between filter width and spectral centers in turn influenced the design of early swept frequency spectrum analyzers. They were designed around a fixed bandwidth Intermediate Frequency (IF) filter through which spectral regions were probed by shifting them to the filter with a linear time-frequency swept heterodyne.
Spectrum analyzers designed for audio and vibration analysis differ from equal space, equal bandwidth systems in that they were designed to analyze signals where the bandwidths are proportional to the center frequencies. This property is exhibited in the model of the ear as well as other mechanical resonator systems such as vibrating strings and air columns. Analyzers matched to this spectral characteristic are called constant Q analyzers where Q (the quality factor of a filter) is the ratio of a filter's center frequency to its bandwidth.
Stationary and non-stationary signals require different criteria for the proportional factor coupling bandwidth to center frequency. For stationary audio signals such as speech and music, the bandwidth is proportional to the signal center frequency so that two center frequencies an octave apart will have filter bandwidths with a ratio of 2. In order to best analyze and adjust signals with this property, a constant Q filter bank is used. Graphic equalizers and sound boards used for audio recording and playback are common examples of constant Q filter banks.
The spectra of constant Q filter banks are equally spaced and have equal bandwidth on a log scale. This property is useful for tracking harmonics which move unequal intervals in standard spectrum analyzers but move the same interval in a constant Q spectrum analyzer. For instance, if a fundamental tone moves 10% of its center frequency, its first harmonic moves 20% and its second harmonic moves 40%.
For non-stationary signals, the bandwidths are chosen to be proportional to the square root of the center frequency so that two center frequencies an octave apart have filter bandwidths with a ratio of √2. The square root proportional bandwidth spectrum analyzer offers the maximum integration gain for linearly varying FM sweeps. Investigators of dolphin communication signals, which are linear FM sweeps, use this form of spectrum analyzer.
Another important difference between standard and proportional bandwidth spectrum analyzers is the spectral range. The frequency range of audio and vibration signals span multiple decades rather than multiple octaves. Therefore there is a need for better proportional bandwidth spectrum analyzers.